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Academic literature on the topic 'Hindu Arithmetic'

Author: Grafiati

Published: 26 July 2024

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Journal articles on the topic "Hindu Arithmetic"

1

Folkerts, Menso. "Early Texts on Hindu-Arabic Calculation." Science in Context 14, no. 1-2 (June 2001): 13–38. http://dx.doi.org/10.1017/s0269889701000023.

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This article describes how the decimal place value system was transmitted from India via the Arabs to the West up to the end of the fifteenth century. The arithmetical work of al-Khwārizmī's, ca. 825, is the oldest Arabic work on Indian arithmetic of which we have detailed knowledge. There is no known Arabic manuscript of this work; our knowledge of it is based on an early reworking of a Latin translation. Until some years ago, only one fragmentary manuscript of this twelfth-century reworking was known (Cambridge, UL, Ii.6.5). Another manuscript that transmits the complete text (New York, Hispanic Society of America, HC 397/726) has made possible a more exact study of al-Khwārizmī's work. This article gives an outline of this manuscript's contents and discusses some characteristics of its presentation.

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2

Yong, Lam Lay. "The Development of Hindu-Arabic and Traditional Chinese Arithmetic." East Asian Science, Technology, and Medicine 13, no. 1 (July 5, 1996): 35–54. http://dx.doi.org/10.1163/26669323-01301004.

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Danna, Raffaele. "Figuring Out." Nuncius 36, no. 1 (January 13, 2021): 5–48. http://dx.doi.org/10.1163/18253911-bja10004.

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Abstract The paper focusses on the spread of Hindu-Arabic arithmetic among European practitioners. The analysis is based on an original database recording detailed information on over 1200 practical arithmetic manuals, both manuscript and printed. This database provides the most detailed reconstruction available of the European tradition of practical arithmetic from the late 13th to the end of the 16th century. The paper argues that studying this spread makes it possible to open a perspective on a progressive transmission of ‘useful knowledge’ from the ‘commercial revolution’ to the ‘little divergence’. Focussing on the transmission of practical arithmetic allows to stress the role of skills and human capital in pre-modern European economic development. Moreover, it allows to reconstruct a progressive transmission, from the Mediterranean to the Atlantic, of a ‘practical knowledge’ which eventually contributed to major developments in European ‘theoretical knowledge’.

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Brown, Peter B. "Muscovite Arithmetic in Seventeenth-Century Russian Civilization: Is It Not Time to Discard the “Backwardness” Label?" Russian History 39, no. 4 (2012): 393–459. http://dx.doi.org/10.1163/48763316-03904001.

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Muscovite civilization utilized Byzantine-Greek alphanumerals for its mathematical symbols. Occasionally derided by historians for being retrograde in comparison to the Hindu-Arabic numerals sixteenth- and seventeenth-century Europe adopted, Muscovy’s alphanumerals were versatile and suitably contoured to perform a variety of computational tasks. Muscovite alphanumerals were an integral part of early Moderen Russia’s administrative culture, and played a prominent role in fostering the experiential knowledge underlying the educational achievements of the Imperial Period. Though they lacked the zero and the decimal, Muscovites still had a reasonable grasp of the base-ten system, and comprehended well basic arithmetical skills and relationship properties, less so equational ones. The Russians developed complex abaci well suited for commercial transactions, large-scale construction, military inventories and payrolls, and the land registry, to name a few. These instruments manipulated an extensive variety of weights, measures, linear distances, area dimensions, volume measurements, and currency. Muscovite arithmetic was a prominent factor assisting in the advancement of critical thinking skills in 1600’s Russia. Nonetheless, as the seventeenth century wore on, sociological, educational or pedagogical, military scientific, administrative, and cultural arguments or interactive phenomena came to bear and increasingly found the Muscovite algorithmic symbols wanting. In 1699 the government decreed that Hindu-Arabic numerals henceforth were to be used in official documents throughout the country. Directly and indirectly, the complex thought processes bound up when operating with Muscovite alphanumerals were one impetus for the further unfolding of Russian civilization after 1700.

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Lauber, Murray. "Casting Out Nines: An Explanation and Extensions." Mathematics Teacher 83, no. 8 (November 1990): 661–65. http://dx.doi.org/10.5951/mt.83.8.0661.

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The method of casting out 9s has been used for centuries, perhaps even as long as a millenium, for checking computations with integers involving the four mathematical operations. According to Eves (1980, 160–68) it was used by Hindu-Arabic scholars in the Middle Ages. It appears to have been imbibed by Western culture as a part of the decimal system of representation of numbers. With the invention of the electronic calculator its practical value has diminished. However, it is still an intriguing application of modular arithmetic that can be generalized to arithmetic in other bases. This article explains how casting out 9s is done, examines some reasons for including it as a topic for exploration in the mathematics curriculum, and uses modular arithmetic to explore its mathematical basis and its generalizability to computations in bases other than ten. A method of detecting errors in the transmission of computer code with some affinities to its analogues is also explored.

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León Corredor, Olga Lucía, and Dora Inés Calderón. "Bilingualism of Colombian Deaf Children in the Teaching-Learning of Mathematics in the First Year of Elementary School." Colombian Applied Linguistics Journal 12, no. 2 (April 11, 2011): 9. http://dx.doi.org/10.14483/22487085.80.

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This paper summarizes some results of the first ethnographic research study conducted in Colombia in three different elementary schools for deaf children in which bilingualism (sign-language and written-language) is starting to be emphasized. This study focuses on the teaching of mathematics in classrooms for deaf children using contexts proclaimed as bilingual. The participants in the study were first grade teachers. The analysis presented in this paper illustrates the struggles that teachers experience teaching arithmetic in such a context. The teaching of arithmetic using bilingualism requires three types of semiotic registers: sign-language and written-Spanish, and the Hindu-Arabic numeration system. The analysis indicates some puzzling teaching learning issues interweaving language and mathematics. These issues are of linguistic and communicative, social and cultural, and cognitive and pedagogical nature.

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Lo, Steson, and Sally Andrews. "The effects of mental abacus expertise on working memory, mental representations and calculation strategies used for two-digit Hindu-Arabic numbers." Journal of Numerical Cognition 8, no. 1 (March 31, 2022): 89–122. http://dx.doi.org/10.5964/jnc.8073.

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In Asia, some children are taught a calculation technique known as the ‘mental abacus’. Previous research indicated that mental abacus experts can perform extraordinary feats of mental arithmetic, but it disagrees as to whether the technique improves working memory. The present study extended and clarified these findings by contrasting performance from several numerical and working memory tasks across three groups of participants: Japanese mental abacus experts, abacus-naïve Australian undergraduates, and abacus-naïve Japanese undergraduates. It also investigated whether the mental representations and strategies used to process two-digit numbers differed across the three groups. First, the results showed that the Japanese mental abacus experts only performed better when the numerical and working memory tasks involved arithmetic problems, suggesting domain-specific transfer rather than domain-general improvements to numerical processing or working memory. Second, the results suggest that the Japanese mental abacus experts were less reliant on decomposed magnitude representations, and used a processing strategy that is less sensitive to the perceptual overlap between numbers. Finally, performance was less discrepant between the Australian and Japanese abacus-naïve undergraduates than either group with the Japanese mental abacus experts, indicating that mental abacus training, rather than socio-cultural differences, was responsible for the observed group differences.

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Elman, Benjamin A. "Jesuit Scientia and Natural Studies in Late Imperial China, 1600-18001." Journal of Early Modern History 6, no. 3 (2002): 209–32. http://dx.doi.org/10.1163/157006502x00130.

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AbstractArguably, by 1600 Europe was ahead of China in producing basic machines such as clocks, screws, levers, and pulleys that would be applied increasingly to the mechanization of agricultural and industrial production. In the seventeenth and eighteenth centuries, however, Europeans still sought the technological secrets for silk production, textile weaving, porcelain making, and large scale tea production from the Chinese. Chinese literati in turn, before 1800, borrowed new algebraic notations (of Hindu-Arabic origins), Tychonic cosmology, Euclidean geometry, spherical trigonometry, and arithmetic and trigonometric logarithms from Europe. Until 1990, Chinese elites and their Manchu rulers interpreted the transition in early modern Europe—from new forms of scientific knowledge to new modes of industrial power—on their own terms. Each side made a virtue out of the mutually contested accommodation project, and each converted the other's forms of natural studies into acceptable local conventions of knowledge. The Ming and Qing imperial court induced Jesuit calendrical, military, and land mensuration experts to work as imperial minions in the government bureaucracy to augment each dynasty's own project of political and cultural control. Consequently, it would be a historiographical mistake to underestimate Chinese efforts to master on their own terms the Western learning of the Jesuits in the sixteenth, seventeenth, and eighteenth centuries.

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Timsina, Ashmita, Uday Kumar Thera, and Naveenkumar Ramasamy. "Phenotypic Screening of F3 Rice (Oryza sativa L.) Population Resistance Associated with Sheath Blight Disease." International Journal of Bio-resource and Stress Management 13, no. 5 (May 31, 2022): 527–34. http://dx.doi.org/10.23910/1.2022.2877.

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The experiment was conducted during July–December, 2019 in the Agricultural Research Farm Institute of Agricultural Sciences, Banaras Hindu University, Varanasi, Uttar Pradesh, India. One hundred and twenty-two F3 rice populations from the cross made between IC277332 (susceptible parent)×IC277275 (moderately resistant parent) were evaluated against sheath blight disease under field conditions. The area under disease progress curve (AUDPC) values categorized rice population into four groups viz., moderately resistant (24), moderately susceptible (38), susceptible (40), and highly susceptible (20). A moderate resistance level to the disease was identified during the study in 24 lines (19.6%) with a mean Percentage Disease Index (PDI) of 12.22%−36.6%. Furthermore, 38 individuals showed moderate susceptibility with AUDPC values (1012−1446 day-1). The maximum PDI and AUDPC value were 76.11 and 2325.56, and the minimum PDI and AUDPC values were 22.78 and 622.22, respectively. The principal component (PCA) biplot analysis showed 71.62% and 12.05% variation, respectively. Unweighted Pair Group Method of Arithmetic Means (UPGMA) cluster analysis grouped the 122 individuals into two major clusters, A and B and sub-clusters. These findings indicated that no rice line resistant to sheath blight had been identified. However, few population lines exhibited moderate resistance, which can be utilized as donor lines to generate sheath blight-resistant rice cultivars. These findings will provide a solid basis for our future breeding and screening activities at the institution.

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ASSAYAG, JACKIE. "Spectral Secularism: Religion, Politics and Democracy in India." European Journal of Sociology 44, no. 3 (December 2003): 325–56. http://dx.doi.org/10.1017/s0003975603001310.

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Everyone invokes secularism in India. So the spectrum of secularism is very large. However, it is rather the spectral ideas of “majority” (hindus) and “minorities” (Muslims, Christians) conceived in demographic (rather than political) terms which characterizes the discussion of this question. The insistence of Hindu nationalists on emphasizing that they are the majority tend to blur the difference between Hindu identity and Indian identity, coextensive with the territory of India. This concept, moreover, serves them in their legitimating of the democratic system insofar as the arithmetical rule is a first principle of this political regime. In the name of a secularism founded on the idea of the greater number (and also the supposed ideal of immemorial Hindu tolerance) India must be governed in accordance with demographic fact defined in religious terms. One of the paradoxical consequence of this “majoritarianism” is the development of “majority minority complex” of the Hindus and the increasing hate and violence (against Muslims and Christians). Today, the Hindu nationalism programme effectively dominates public debate. Its partisans has succeeded in discriminating between “friends” and “foes”, those inside and those outside, those whom one holds dear and those whom one pillories on the basis of a real or imaginary menace weighing upon autochthony, culture, religion and race, and the national (state) sovereignty.

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Books on the topic "Hindu Arithmetic"

1

Speed arithmetic: Based on Vedic word-formulas. 3rd ed. Chennai: Vijaya Ramasubban, 2008.

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The Arithmetic of Al-Uqlīdisī: The Story of Hindu-Arabic Arithmetic as told in Kitāb al-Fuṣūl fī al-Ḥisāb al-Hindī. Springer, 2011.

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3

Saidan, A. S. The Arithmetic of Al-Uqlidisi: The Story of Hindu-Arabic Arithmetic as told in Kitab al-Fusul fi al-Hisab al-Hindi. Springer, 2011.

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4

Taylor, John, and Bhascara Acharya. Lilawati; or a Treatise on Arithmetic and Geometry. University of Cambridge ESOL Examinations, 2014.

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5

Taylor, John, and Bhascara Acharya. Lilawati; or a Treatise on Arithmetic and Geometry. University of Cambridge ESOL Examinations, 2013.

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6

Saidan, A. S. Arithmetic of Al-Uqlīdisī: The Story of Hindu-Arabic Arithmetic As Told in Kitāb Al-Fuṣūl Fī Al-ḤIsāb Al-Hindī. Springer London, Limited, 2012.

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Book chapters on the topic "Hindu Arithmetic"

1

Danna, Raffaele. "The spread of Hindu-Arabic numerals among practitioners in Italy and England (13th-16th c.): two moments of a European innovation cycle?" In L’economia della conoscenza: innovazione, produttività e crescita economica nei secoli XIII-XVIII / The knowledge economy: innovation, productivity and economic growth, 13th to 18th century, 59–87. Florence: Firenze University Press, 2023. http://dx.doi.org/10.36253/979-12-215-0092-9.06.

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Together with introducing a set of key innovations in commercial practices, the merchant-bankers of the commercial revolution of the 13th century were also the first European economic agents to adopt Hindu-Arabic numerals. As practical arithmetic provided the mathematical foundation for commercial innovations, studying its European spread provides a particularly suitable angle to study the diffusion of practical knowledge in the pre-modern period. Italy was the early adopter of these techniques, while in England these practices became widespread at the onset of the little divergence. In this paper, I discuss in comparative perspective the social diffusion of this knowledge in Italy and England, and its wider impact. On the one hand, this analysis makes it possible to show a number of parallels between the trajectories followed by these societies. On the other hand, it allows to observe the complex interactions between practical knowledge and wider economic, institutional, and social changes.

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2

"Conversion and the Arithmetic of Religious Communities." In Hindu Nationalism, 233–54. Princeton University Press, 2009. http://dx.doi.org/10.2307/j.ctt7s415.18.

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"13. Conversion and the Arithmetic of Religious Communities." In Hindu Nationalism, 233–54. Princeton University Press, 2009. http://dx.doi.org/10.1515/9781400828036.233.

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4

Kline, Morris. "Arithmetic and Algebra in the Sixteenth and Seventeenth Centuries." In Mathematical Thought from Ancient to Modern Times, 250–84. Oxford University PressNew York, NY, 1990. http://dx.doi.org/10.1093/oso/9780195061352.003.0013.

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Abstract The first major new European mathematical developments took place in arithmetic and algebra. The Hindu and Arabic work had put practical arithmetical calculations in the forefront of mathematics and had placed algebra on an arithmetic instead of a geometric basis. This work also attracted attention to the problem of solving equations.

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"Arithmetic: Hindu-Arabic Numbers and the Rise of Commerce." In The Great Rift, 139–56. Harvard University Press, 2018. http://dx.doi.org/10.4159/9780674985186-009.

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6

Denniss, John. "Learning arithmetic: textbooks and their users in England 1500–1900." In The Oxford Handbook Of The History Of Mathematics, 448–67. Oxford University PressOxford, 2023. http://dx.doi.org/10.1093/oso/9780199213122.003.0020.

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Abstract Numbering’, ‘reckoning’, ‘cyphering’, and even ‘arithmetic’ itself are words that now have an archaic ring to them, but for centuries there have been textbooks entirely devoted to these subjects. As the Hindu-Arabic numerals began to pass westwards from Baghdad in the ninth century they were accompanied by treatises that explained how to write and use them. In the Latin West such treatises became known as ‘Algorisms’ (after al-Khwārizmī, the author of the best known of them), and their contents became the essential core of all later textbooks on arithmetic for many centuries.

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Mazur, Joseph. "Refuting Origins." In Enlightening Symbols. Princeton University Press, 2016. http://dx.doi.org/10.23943/princeton/9780691173375.003.0008.

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This chapter discusses the debate among experts over the origins of the Hindu-Arabic numerals. One such expert was the French mathematician and historian Michel Chasles, who argued that by the fifth century, France already had a decimal place-value system for computations documented in Boethius's Arithmetic, which seemed to use a multiplication table with Arabic numbers. For much of the nineteenth century, the Indian origin of positional decimal notation had been challenged. The chapter also considers the claim made by George Rusby Kaye in 1907 that the numerals and the decimal system could not have been Indian in origin and that the history of Hindu-Arabic number representation was complicated by the existence of so many forgeries of the time. Whatever the truth, it is quite likely that sometime in the fifth century, Indian numbers had come to Alexandria via a trade route through Syria before moving westward.

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Mee, Nicholas. "Burning Down the House." In Celestial Tapestry, 69–77. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198851950.003.0008.

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Algorithms are important in the modern world, but what is an algorithm? At school we learn algorithms called arithmetic, which is much easier in Hindu–Arabic rather than Roman numerals. Chaucer calls them augrim numbers. Augrim is a variant of algorithm and derives from the name of the ninth-century Persian mathematician al-Khwārizmī. In ‘The Miller’s Tale’ Chaucer tells of the scholar Nicholas with his augrim stones and astrolabe. This could be a caricature of Nicholas of Lynn. There was a long rivalry between those who performed calculations using arithmetic and those who used a counting table. The Exchequer gets its name from the similarity between a chess board and the counting table used to calculate taxes. For many centuries, debts were recorded on tally sticks. In 1834 the Houses of Parliament were destroyed when the vast collection of accumulated tally sticks were burnt, and the fire was immortalized by J. M. W. Turner.

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Ahmad, Irfan. "Hindu Orientalism: The Sachar Committee and Over-representation of Minorities in Jail." In The Politics of Muslim Identities in Asia, 115–44. Edinburgh University Press, 2021. http://dx.doi.org/10.3366/edinburgh/9781474466837.003.0008.

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With the release in 2006 of the Sachar Committee Report (SCR), instituted by the Government of India, the social-economic backwardness of Muslims became a public issue. Discussing responses to the SCR, this chapter sheds light on the interrelationships among democracy, minorities and ‘inclusive development’. The principal contention is that behind the reluctant, perhaps even insincere, implementation of the SCR under the Congress administration and its near dumping under the Modi administration was the successful mobilisation of Re-Orientalism. This Re-Orientalism – or what Mita Banerjee, Lisa Lau and Ana Mendes allude to as ‘Hindu Orientalism’ – stigmatised the relative deprivation of Muslims vis-à-vis other communities by deploying tropes of ‘Islamic terrorism’, ‘fanaticism’, ‘Muslim appeasement’, ‘separatism’, ‘disloyalty to the nation’ and so on – tropes supplied by British colonialism. That this Re-Orientalism won was not inevitable. An anti-Orientalist alternative notion of democracy – democracy as an ethos resonant with suffering and mutual care – did exist, but it was sacrificed to prolong the ceremonial, mediatised, arithmetic, corporate national democracy. The chapter conclude with theoretical observations about the limits and possibilities of the term ‘Re-Orientalism’.

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Budd, C. J., and C. J. Sangwin. "Doing the sums." In Mathematics Galore!, 222–50. Oxford University PressOxford, 2001. http://dx.doi.org/10.1093/oso/9780198507697.003.0009.

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Abstract In Chapter 7 we looked at ways of writing whole numbers. The Hindu system of number bases, which we still use, turned out to be ideal and negative number bases are an interesting modem development. In this chapter we will introduce the logarithm. The discovery of the logarithm, by John Napier, was perhaps the most important advance in practical calculation methods after the introduction of the Hindu, decimal number system. The logarithm, like many things in mathematics, turns out to have a much deeper significance and greater use than simply helping us calculate. In the second half of this chapter we go on to describe a practical implementation of logarithms: the slide rule. The slide rule is also an example of what is known as an analogue computer. Most modem computers are digital and they store and manipulate information as strings of ones and zeros. We saw binary arithmetic in Chapter 7. Some computers, in particular early computers, were not digital and used other technologies, such as flowing liquids or mechanical links. The importance of these things are now becoming forgotten, particularly with the rise of the electronic calculator. We ask you to do as many of the exercises as you can with only paper and pencil. Of course, your calculator is useful to help you to check your answers.

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Conference papers on the topic "Hindu Arithmetic"

1

MARCHITAN, Gabriela. "Istoria Didacticii Matematicii civilizației Indiei Antice." In Inter/transdisciplinary approaches in the teaching of the real sciences, (STEAM concept) = Abordări inter/transdisciplinare în predarea ştiinţelor reale, (concept STEAM). Ion Creangă Pedagogical State University, 2023. http://dx.doi.org/10.46727/c.steam-2023.p114-117.

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The creation of Hindu mathematicians had an enormous influence on the subsequent evolution of arithmetic (the Hindu positional decimal number system), algebra (dispersion method for solving indeterminate equations of the first and second degree with two unknowns) and trigonometry (infinite strings for sine, cosine and arctangent). The earliest information with reference in Ancient India relates to the era of the composition of the philosophical-religious holy books "The Vedas".

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2

Babekir, Mohammed Elbasheir Mohammed, and Laurie Butgereit. "Results of smart device based arithmetic competition in Blue Nile State, Sudan, in Hindi-Arabic script." In 2017 IST-Africa Week Conference (IST-Africa). IEEE, 2017. http://dx.doi.org/10.23919/istafrica.2017.8102285.

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